What is x/(x^2-4)< 1/3 ?

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x/(x^2-4)< 1/3

\frac{x}{x ^{2} - 4} < \frac{1}{3}

x < - 2 or - 1 < x < 2 or x > 4

Interval Notation

(- \infty, - 2) \cup (- 1, 2) \cup (4, \infty)

Solution steps

\frac{x}{x ^{2} - 4} < \frac{1}{3}

Rewrite in standard form

\frac{3 x - ( x + 2 ) ( x - 2 )}{( x + 2 ) ( x - 2 )} < 0

Factor

\frac{3 x - ( x + 2 ) ( x - 2 )}{( x + 2 ) ( x - 2 )} : \frac{- ( x + 1 ) ( x - 4 )}{( x + 2 ) ( x - 2 )}

\frac{- ( x + 1 ) ( x - 4 )}{( x + 2 ) ( x - 2 )} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 1 ) ( x - 4 ) ) ( - 1 )}{( x + 2 ) ( x - 2 )} > 0 \cdot (- 1)

Simplify

\frac{( x + 1 ) ( x - 4 )}{( x + 2 ) ( x - 2 )} > 0

Identify the intervals

x < - 2 or - 1 < x < 2 or x > 4

\frac{5}{6} + \frac{3}{4}

- 4 (y + 7) = 2 (- 2 y - 9) - 10

5^{- 5} \cdot 5^{- 3}

4 (x - 1)^{2} + 2 = 10

x^{3} - x \geq 0

What is x/(x^2-4)< 1/3 ?
The solution to x/(x^2-4)< 1/3 is x<-2\lor-1<x<2\lor x>4